A New Nite-volume Approach for the Solution of Convection-diiusion Problems

For the unsteady convection-diiusion equation in two dimensions we derive a new cell-based semi-discretization which is founded on the method of lines and a nite volume approach. Moreover, we present a second semidiscretization technique, a nonconforming Petrov-Galerkin method with exponentially tted trial and test functions. If we use appropriate quadrature rules both approaches are equivalent. We obtain diierential-algebraic equations of index 1 and present consistency, stability and convergence properties for these semidiscrete systems. For the time integration we use implicit methods and state the convergence of the fully discrete systems. Finally, we consider several test problems and present numerical results concerning the quality of our discretization method.